# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#7

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Question

An athlete prepares for a race by completing a practice run on each of 11 consecutive days. On  each day after the first day, he runs further than he ran on the previous day.

The lengths of his 11 practice runs form an arithmetic sequence with first term a km and common  difference d km.

He runs 9 km on the 11th day, and he runs a total of 77 km over the 11 day period.

Find the value of a and the value of d.

Solution

We are given that the lengths of athlete’s 11 practice runs form an arithmetic sequence with first  term a km and common difference d km, we can write the following information.

Therefore, we can write that;

We are given that;

Expression for the general term  in the Arithmetic Progression (A.P) is:

Therefore, 11th term can be written as;

We are also given that;

Since, the lengths of athlete’s 11 practice runs form an arithmetic sequence; we can utilize the  expression sum of arithmetic series to find the total distance run by athlete in 11 days.

Expression for the sum of  number of terms in the Arithmetic Progression (A.P) is:

Therefore;

This value of  can be substituted in following equation obtained above to find the value of .